:{52 ON THE RESISTANCE TO TORSION OF CERTAIN FORMS OF SHAFTIM: 

 The values of the " efficiency " are easily obtained. 



TABLE of E. 



The above results do not need any detailed discussion. We see that in all cases 

 the maximum stress is greater than the maximum stress for the circular section. 

 Also the efficiency is always less than unity. If we compare these values of the 

 efficiency with those in 19, we see that, on the whole, the rule holds that the more 

 compact the section the higher its efficiency. On the other hand, by indenting a 

 section we render it less efficient. 



24. Conclitsion and Summary, 



Looking back upon the results of the paper, we see that the study of these special 

 forms of cross-section sheds new light upon several little-explored parts of the theory 

 of elasticity. 



It confirms to a great extent DE SAINT-VENANT'S investigations concerning the 

 l>ehaviour under torsion of a rail, or of shafts of similar section. 



Owing to the great generality of the forms treated, it enables us to correlate the 

 results previously obtained for sections of various shapes, especially with regard to 

 the maximum stress. It shows us what type of cross-section will give us four fail- 

 points not at the points of the contour closest to the centre ; within what limits we 

 may expect to find this exception to the ordinary rule ; and in what manner this case 

 passes into others. 



Again, with regard to the effect of keyways upon the torsional rigidity, the results 

 of the paper tell us that, without risk of sensible error, we may in practice, in order 

 to get the joint effect of two indefinitely thin keyways or slits, add the known effects 

 of each key way, taken separately. 



Further, these results bring the theory of elasticity into better accordance with 

 observed facts, by showing that the effects of keyways of moderate depth are 

 comparatively much smaller than would have been expected from the results for the 

 circle. 



